Question: Simplify the following expression: $a = \dfrac{-10r^2 + 90r + 100}{r - 10} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-10$ , so we can rewrite the expression: $ a =\dfrac{-10(r^2 - 9r - 10)}{r - 10} $ Then we factor the remaining polynomial: $r^2 {-9}r {-10} $ ${-10} + {1} = {-9}$ ${-10} \times {1} = {-10}$ $ (r {-10}) (r + {1}) $ This gives us a factored expression: $\dfrac{-10(r {-10}) (r + {1})}{r - 10}$ We can divide the numerator and denominator by $(r + 10)$ on condition that $r \neq 10$ Therefore $a = -10(r + 1); r \neq 10$